Question

Differentiate among ratios, proportions, and rates as used in epidemiology today. Define each of these measurements, and briefly describe its importance in community health.

Answer 1

Ratios -

Ratios are simply expressions of one measure relative to another. There are several types of ratios that are frequently used in public health.

Simple Ratios Example -

Consider a class that has 20 male students and 80 female students. We can think about this in several ways. We could express this simply as the ratio of men to women and write the relationship as 20:80 or 20/80. We can also simplify this by dividing both the numerator and the denominator by a number that divides evenly into both the numerator and the denominator. In this case, we could divide both by 20 to simplify this to a 1:4 ratio (or 1/4 ratio). This indicates that for every man, there are four women.

We could also consider this from the inverse perspective, i.e., the number of women relative to the number of men; in this case the ratio of women to men is 80/20 which is equivalent to 4 to 1, i.e., there are four women for every man.

Proportions -

A proportion is a type of ratio that relates a part to a whole. For example, in the class with with 20 men and 80 women, the total class size is 100, and the proportion of men is 20/100 or 20%. The proportion of women is 80/100 or 80%. In both of these proportions the size of part of the class is being related to the size of the entire class. The class above conveniently had a total size of 100, but this usually isn't the case.

If we go back to the information on mortality from bird flu that was presented on the previous page, it can be seen that there are several ways of thinking about this basic information.

The fact that 44 died and the other 79 lived could be expressed as a simple ratio, which compares the number who died to the number who survived. 44/79 or 44:79 would be two ways of expressing this simple ratio. The ratio of those who died relative to those who lived was 44 to 79.

Alternatively, we might want to focus on the proportion who lived. In total, 123 people were infected, and 44 of these died. Therefore, the proportion who died was 44/123, which could be expressed as a decimal fraction (0.36) or as a percentage (36%). This proportion is referred to as the "case-fatality" rate, although strictly speaking, it is a proportion and not a rate.

Rate -

Rates are a special type of ratio that incorporate the dimension of time into the denominator. Familiar examples include measurements of speed (miles per hour) or water flow (gallons per minute).

Example 1

If a car travels 24 miles in 2 hours, its average speed is a rate of 24 miles/ 2 hours = 12 miles/hr.

Example 2:

Suppose a car traveled 24 miles in 2 hours, then continued and traveled miles in 3 hours, and then another 12 miles in 1 hour.

We can compute the average rate of speed for the entire trip by adding up the total distance covered and dividing it by the total time that the trip took.

Average speed for the trip = (24 miles + 24 miles + 12 miles) / (2 hour + 3 hours +1 hour) = 60 miles / 6 hours = 10 miles per hour

Note that some commonly used measurements of health outcomes are referred to as "rates" even though they are actually proportions.

For example:

- A mortality rate is the proportion of deaths occurring over a span of time in a population.  

- An attack rate is the proportion of people developing an infectious disease after exposure to a pathogen.

- A case-fatality rate is the proportion of individuals who die after developing a disease.

Strictly speaking, these are all proportions, but incidence rates or incidence density is a measurement of the frequency of a health outcome that is more like a true rate. An incidence rate basically quantifies the number of health outcomes and the total exposure time (i.e., time at risk) in a group or population. Similar to computation of an average speed for an automobile, an incidence rate is computed by dividing the total number of health-related events that occurred by the total exposure time at risk for the group.